Orlik and Raymond [1]} (Davis and Januszkiewicz [2]}) proved that any toric 4-manifold is (non-equivariantly) homeomorphic to a connected sum of copies
of \(\mathbb {C}P^{2},\overline{\mathbb {C}P}^{2}\)  and \(S^{2}\times S^{2}\) .
According to Buchstaber and Panov [3]} with \(n=2\)  (e.g.
[4]}, [5]}), if \(M\)  is a toric 4-manifold and if \(\left\lbrace  \alpha _{1},\cdots ,\alpha _{k}\right\rbrace  \)  is the canonical basis of \(H^{2}(M)\) , then the manifold \(M(\alpha _{{\small 1}},\cdots ,\alpha _{{\small k}})\)  is diffeomorphic to \(Q_{k}\) . We extend
this phenomina to all 1-connected topological 4-manifolds.
